Dear Stackexchange users,
given that the negative interest rates on a lot of sovereign bonds with maturity under 10 years are trading in the negative (nominal) interest rate territory (recently also ...

Consider the following plot, courtesy of this page:
Regarding the $y$-axis, how does this "expected return" relate to the "instantaneous expected return" in a geometric Brownian motion (GBM)?
E.g., ...

I will write a test based on Excel and one of the topics is "The Asset Liability related analysis: including the input assumptions generation, constraints, portfolio optimization analysis and results ...

So there are two assets with return rates $r_1$ and $r_2$ which have identical variances and a correlation coefficient $p$. The risk free rate is $r_f$.
I need to find an expression for the optimal ...

My overall goal is to find an efficient frontier using QP in terms of $\alpha$ and residual variance ($\omega^2$) for a portfolio $P$ given a benchmark $B$.
We know the equation for residual variance ...

Having read a chapter in Bodie, Kane and Marcus' Investment, I came across a formula I do not quite understand. It states that the percentage fee in excess of what an index fund would charge on active ...

This question is related to recent rule changes in the Quantopian Open.
I am trying to figure out a closed form solution to a beta constrained minimum variance portfolio problem but it doesn't seem ...

I was reading about MPT http://en.wikipedia.org/wiki/Modern_portfolio_theory and notices that the total variance of a portfolio is $x' \Sigma x$, where x is the weighting of the assets and $\Sigma$ ...

I am studying the Markowitz portfolio optimization theory, and I just wanted to ask if I understood this correctly. For a stock portfolio we distinguish two kinds of risks: an unsystematic risk, which ...

New here and I have a question that may be very basic but despite my research I cannot connect the dots.
I would like to know how to connect the nxn asset covariance matrix for an efficient tangency ...

I want to calculate the efficient frontier for a set of 140 assets using returns from the past 10 years. However, some of these assets came into existence only more recently, so for some assets I have ...

What is a coherent risk measure, and why do we care? Can you give a simple example of a coherent risk measure as opposed to a non-coherent one, and the problems that a coherent measure addresses in ...

How does the answer to this question Risk minimization by investing in all assets with positive expected return change if assets can be positively correlated (but not perfectly) and short sales are ...

Suppose I have a stock selection universe of 100 stocks.
I have estimated the covariance matrix of this 100 stocks.
I would like to create an equaly-weighted basket of 5 stocks which has the lowest ...

This question is bothering me for a while. We suppose a very simple and basic set up. Given are a certain amount of assets from which we want to build an portfolio in an "optimal sense". MPT gives us ...

I am following Risk and asset allocation (Attilio Meucci,2007). I must say I am enjoying this reading quite a lot so I hope nobody takes my question as a critique on the text.
When we are introduced ...

In Black-Litterman we get a new vector of expected returns of the form:
\begin{align}
\Pi_{BL} = \Pi + \underbrace{\tau \Sigma P^T[P\tau\Sigma P^T+\Omega]^{-1}}_{\text{correction}}[Q-P\Pi]
\end{align}
...

In an attempt to learn Black-Litterman I have come across this "simple" example. Suppose that you analyze market data using CAPM
$$r_i-r_f=\beta_i(r_m-r_f)+\epsilon_i$$
Suppose there are 2 assets in ...

If I have three asset classes and their historical weekly returns for five years, how can I construct a minimum variance portfolio and an efficient frontier plot with Excel? To do that do I have to ...

I'm trying to learn Black-Litterman. I feel like I get the overall idea from books like Risk and Asset Allocation by Meucci as well as some of the early papers which develop the model. What I would ...

I need help about portfolio optimization in R. I have inverted matrix and I want to use it as an input in portfolio optimization. It was non-positive definite before I have handled it. In portfolio ...

When using asset pricing models such as the CAPM or the Fama-French four factor model to determine the risk-adjusted return of a portfolio, does this strictly require efficient diversification of the ...

For a problem where we need to optimize the portfolio based on the data, going for Markowitz MPT has the following advantage: we only have to estimate mean and covariance to find optimal weights. I'd ...

I'm trying to calculate the efficient frontier (and the optimal portfolio at the Sharpe ratio) given two vectors for a portfolio: (1) expected returns and (2) historical standard deviations. I would ...

In Robert Merton's derivation of the efficient frontier of a portfolio, he minimizes
$\frac{1}{2}\sigma^2 $ over the investment weights in each asset, where $\sigma^2$ represents portfolio variance. ...